There have been numerous attempts to provide a coherent system to allow for an improved way to accurately render the human body. A method for measuring the physical attributes of the human body proposed by Leonardo DaVinci is referenced by Curtin, U.S. Pat. No. 4,823,476, Apr. 25 1989. Curtin provides a static transparent panel that divides the body into predetermined segments. The invention fails to provide an adjustable means of measuring and transferring the details of proportion that are intrinsic to the golden section.
U.S. Pat. No. 5,174,037, Dec. 29, 1992, Curtin provides a similar method for measuring the human head. This is also a static grid that fails to disclose the golden section.
U.S. Pat. No. 1,280,094, Sep. 24, 1918, Smith describes a method for rendering the human body and head by presenting a grid divided into various-sized diamond shapes. The invention is static and there is no disclosure of the golden section.
U.S. Pat. No. 2,780,004, Mar. 25, 1954, Rosenbaum describes a method for measuring the human head in relation to providing eyeglasses. The device comprises a frame with movable blades that can be aligned to specific features of individual faces. The device is limited to the face and presents no understanding of the golden section.
U.S. Pat. No. 1,462,850, Jul. 24, 1923, Clark describes a profile-defining apparatus. This device provides a series of adjustable components that feature a number of various geometrical possibilities that can be combined to create assorted profiles. There is no disclosure of the golden section.
U.S. Pat. No. 364,043, May 31, 1887, Riche describes an improved pantograph. Riche's device allows for an image to be reduced or enlarged in a manner that can also flip the image on its X axis. The 4 bars of his invention must be attached to a guide track. They are coupled at predetermined points that ignore the principles of the golden section.
U.S. Pat. No. 4,397,090, Aug. 9, 1983, Nicyper describes an improved pantograph that allows for the image being copied to be re-proportioned and/or reversed. To manifest this feature, the 4 bars of his device can be coupled at points that are adjustable. The guide track is also adjustable. Nicyper does not disclose the use of the golden section.
U.S. Pat. No. 834,470, Oct. 30, 1906, Hanssen describes an improved pantograph comprising a triangular frame from which a series of intermediate arms are attached in two sets of equal numbers. The value of each subsequent endpoint increases in intervals of 400. There is no mention of the golden section.
U.S. Pat. No. 3,562,919, Aug. 29, 1968, Green describes a device comprising four arms of a movable parallelogram with one comer attached to a fixed blade featuring a protractor and the opposite comer being confined to move along a straight edge. The device is utilized as a layout tool for a machine shop. There is no relationship to the golden section disclosed.
U.S. Pat. No. 5,867,588, Feb. 25, 1989, Marquardt describes a grid to be placed over an image of the human face for the purposes of facial identification and to determine what constitutes beauty. Marquardt discloses a grid composed of interrelated pentagons and five-pointed stars. Points along the grid are then correlated with various aspects of individual facial features. This process reflects back to DaVinci's understanding of man's relationship to the five-pointed star exemplified in the famous drawing of a man inscribed in a five-pointed star with his limbs outstretched within the circumference of a circle. The golden section is intrinsic in the structure of the pentagon and the five-pointed star. Marquardt is able to correlate positions of the disclosed grid with the golden section for this reason. His invention is static and only applicable to a frontal view of the human face.
The golden section refers to a well-established mathematical ratio that relates segments of different sizes to each other. The golden section is the division of a line into two parts where the smallest part of the line is to the largest part of the line as the largest part of the line is to the entire line. If the line in question were to be divided in half, the decimal equivalent would be 0.5. The decimal equivalent of the golden section is 0.618. The square root of five, minus one, divided by two, also expresses its value. A remarkable property of this number is demonstrated by the following two equations: 1/.618=1.618 and 1+.618=1.618. Add 0.618 to one, or divide one by 0.618, either way you get the same answer.